Question

evaluate the limit, if it exists. (if an answer does not exist, enter dn
lim_{t
ightarrow0}\frac{sqrt{5 + t}-sqrt{5 - t}}{t}

Explanation:

Step1: Rationalize the numerator

Multiply numerator and denominator by $\sqrt{5 + t}+\sqrt{5 - t}$.

$$
LATEXBLOCK0
$$

Step2: Simplify the numerator

Simplify $(5 + t)-(5 - t)$ to $2t$.

$$
LATEXBLOCK1
$$

Step3: Cancel out the common factor

Cancel out the common factor $t$ (since $t
eq0$ as we are taking the limit as $t$ approaches 0).

$$
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$$

Step4: Evaluate the limit

Substitute $t = 0$ into the expression.

$$
LATEXBLOCK3
$$

Answer:

$\frac{1}{\sqrt{5}}$